I have a Bucket of Polar Water that's sitting around in a gallery. I get the feeling that it has something to do with that glacier (glacial? idk) elixir you can use to change your pet's color, but I don't know what to do with it or where to go from here. Any advice?

You can use it to make a glacier pet.

You would need to buy a from the year round tab in the Millionaire Center. Then take both the Chalice and the Bucket to Genetech Lab to make a .

At which point you give it to a pet that has a glacier version you like. Or you could sell the potion, or the bucket itself.